On some optimal control problems for the heat radiative transfer equation
ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 425-444. 
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     author = {Manservisi, Sandro and Heusermann, Knut},
     title = {On some optimal control problems for the heat radiative transfer equation},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {425--444},
     publisher = {EDP-Sciences},
     volume = {5},
     year = {2000},
     mrnumber = {1778394},
     zbl = {0952.49035},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2000__5__425_0/}
}
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Manservisi, Sandro; Heusermann, Knut. On some optimal control problems for the heat radiative transfer equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 5 (2000), pp. 425-444. http://www.numdam.org/item/COCV_2000__5__425_0/

[1] F. Abergel and R. Temam, On some control problems in fluid mechanics. Theoret. Computational Fluid Dynamics 1 ( 1990) 303-326. | Zbl

[2] R. Adams, Sobolev Spaces. Academic Press, New York ( 1975). | MR | Zbl

[3] V. Alekseev, V. Tikhomirov and S. Fomin, Optimal Control. Consultants Bureau, New York ( 1987). | MR | Zbl

[4] I. Babuska, The finite element method with Lagrangian multipliers. Numer. Math. 16 ( 1973) 179-192. | MR | Zbl

[5] D.M. Bedivan and G.J. Fix, An extension theorem for the space Hdiv. Appl. Math. Lett. (to appear). | Zbl

[6] N. Di Cesare, O. Pironneau and E. Polak, Consistent approximations for an optimal design problem. Report 98005 Labotatoire d'analyse numérique, Paris, France ( 1998).

[7] P. Ciarlet, Introduction to Numerical Linear Algebra and Optimization. Cambridge University, Cambridge ( 1989). | MR | Zbl

[8] P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam ( 1978). | MR | Zbl

[9] J.E. Dennis and R.B. Schnabel, Numerical methods for unconstrained optimisation and non-linear equations. Prentice-Hall Inc., New Jersey ( 1983). | Zbl

[10] V. Girault and P. Raviart, The Finite Element Method for Navier-Stokes Equations: Theory and Algorithms. Springer-Verlag, New York ( 1986). | MR | Zbl

[11] M. Gunzburger and S. Manservisi, Analysis and approximation of the velocity tracking problem for Navier-Stokes flows with distributed control. SIAM J. Numer. Anal. (to appear). | MR | Zbl

[12] M. Gunzburger and S. Manservisi, The velocity tracking problem for for Navier-Stokes flows with bounded distributed control. SIAM J. Control Optim. (to appear). | MR | Zbl

[13] J. Haslinger and P. Neittaanmäki, Finite Element Approximation for Optimal Shape Design. Wiley, Chichester ( 1988). | MR | Zbl

[14] K. Heusermann and S. Manservisi, Optimal design for heat radiative transfer systems. Comput. Methods Appl. Mech. Engrg. (to appear).

[15] F.P. Incropera and D.P. Dewitt, Fundamentals of Heat and Mass Transfer. Wiley, New York ( 1990).

[16] M. Modest, Radiative heat transfer. McGraw-Hill, New York ( 1993).

[17] O. Pironneau, Optimal shape design in fluid mechanics. Thesis, University of Paris ( 1976).

[18] O. Pironneau, On optimal design in fluid mechanics. J. Fluid. Mech. 64 ( 1974) 97-110. | MR | Zbl

[19] O. Pironneau, Optimal shape design for elliptic systems. Springer, Berlin ( 1984). | MR | Zbl

[20] R.E. Showalter, Hilbert Space Methods for Partial Differential Equations. Electron. J. Differential Equations ( 1994) http://ejde.math.swt.edu/mono-toc.html | MR | Zbl

[21] J. Sokolowski and J. Zolesio, Introduction to shape optimisation: Shape sensitivity analysis. Springer, Berlin ( 1992). | Zbl

[22] T. Tiihonen, Stefan-Boltzmann radiation on Non-convex Surfaces. Math. Methods Appl. Sci. 20 ( 1997) 47-57. | MR | Zbl

[23] T. Tiihonen, Finite Element Approximations for a Beat Radiation Problem. Report 7/ 1995, Dept. of Mathematics, University of Jyväskylä ( 1995).

[24] V. Tikhomirov, Fundamental Principles of the Theory of Extremal Problems. Wiley, Chichester ( 1986). | MR | Zbl